Asymptotic stability of monotone increasing traveling wave solutions for viscous compressible fluid equations with capillarity term

Asymptotic stability of monotone increasing traveling wave solutions is investigated for a class of viscous compressible fluid equations with capillarity term. By using the theory of planar dynamical systems, the existence has been proved for the monotone increasing traveling wave solution. Moreover, through building uniformly a priori energy estimate for the perturbation of the traveling wave solution, we prove that the monotone increasing traveling wave solution is asymptotically stable in H2×H1.